75.6.16 problem 149

Internal problem ID [16772]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 149
Date solved : Tuesday, January 28, 2025 at 09:22:02 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 8

dsolve([diff(y(x),x)-y(x)=-2*exp(-x),y(infinity) = 0],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 10

DSolve[{D[y[x],x]-y[x]==-2*Exp[-x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \]